We investigate spectral properties of a discrete random displacement model, a Schrödinger operator on with potential generated by randomly displacing finitely supported single-site terms from the points of a sublattice of . In particular, we characterize the upper and lower edges of the almost sure spectrum. For a one-dimensional model with Bernoulli distributed displacements, we can show that the integrated density of states has a -singularity at external as well as internal band edges.
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Roger Nichols, Günter Stolz, Spectral properties of the discrete random displacement model. J. Spectr. Theory 1 (2011), no. 2, pp. 123–153DOI 10.4171/JST/6